Properties

Label 255.2.a
Level $255$
Weight $2$
Character orbit 255.a
Rep. character $\chi_{255}(1,\cdot)$
Character field $\Q$
Dimension $11$
Newform subspaces $4$
Sturm bound $72$
Trace bound $2$

Related objects

Downloads

Learn more about

Defining parameters

Level: \( N \) \(=\) \( 255 = 3 \cdot 5 \cdot 17 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 255.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 4 \)
Sturm bound: \(72\)
Trace bound: \(2\)
Distinguishing \(T_p\): \(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(255))\).

Total New Old
Modular forms 40 11 29
Cusp forms 33 11 22
Eisenstein series 7 0 7

The following table gives the dimensions of the cuspidal new subspaces with specified eigenvalues for the Atkin-Lehner operators and the Fricke involution.

\(3\)\(5\)\(17\)FrickeDim.
\(+\)\(+\)\(-\)\(-\)\(2\)
\(+\)\(-\)\(+\)\(-\)\(2\)
\(-\)\(+\)\(+\)\(-\)\(4\)
\(-\)\(-\)\(-\)\(-\)\(3\)
Plus space\(+\)\(0\)
Minus space\(-\)\(11\)

Trace form

\( 11q + 5q^{2} + 3q^{3} + 17q^{4} - q^{5} - 3q^{6} + 8q^{7} + 9q^{8} + 11q^{9} + O(q^{10}) \) \( 11q + 5q^{2} + 3q^{3} + 17q^{4} - q^{5} - 3q^{6} + 8q^{7} + 9q^{8} + 11q^{9} + q^{10} + 12q^{11} + 5q^{12} + 2q^{13} - 8q^{14} - q^{15} + 17q^{16} - q^{17} + 5q^{18} - 4q^{19} - 7q^{20} + 8q^{21} - 12q^{22} + 8q^{23} - 15q^{24} + 11q^{25} - 18q^{26} + 3q^{27} - 8q^{28} + 2q^{29} - 3q^{30} - 8q^{31} - 7q^{32} - 12q^{33} - 3q^{34} + 17q^{36} + 26q^{37} - 28q^{38} + 2q^{39} - 3q^{40} + 6q^{41} - 24q^{42} - 4q^{43} - 12q^{44} - q^{45} - 32q^{46} - 16q^{47} - 3q^{48} + 27q^{49} + 5q^{50} - q^{51} - 58q^{52} + 10q^{53} - 3q^{54} - 12q^{55} - 72q^{56} + 28q^{57} - 34q^{58} - 20q^{59} - 7q^{60} - 14q^{61} - 64q^{62} + 8q^{63} - 19q^{64} + 18q^{65} - 8q^{66} - 4q^{67} - 7q^{68} - 16q^{69} - 12q^{70} + 9q^{72} + 38q^{73} - 10q^{74} + 3q^{75} - 8q^{76} + 6q^{78} - 16q^{79} + q^{80} + 11q^{81} - 6q^{82} - 4q^{83} - 4q^{84} + 3q^{85} + 44q^{86} - 6q^{87} - 12q^{88} + 38q^{89} + q^{90} - 8q^{91} + 56q^{92} + 24q^{93} + 20q^{94} - 20q^{95} - 23q^{96} + 30q^{97} + 61q^{98} + 12q^{99} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(255))\) into newform subspaces

Label Dim. \(A\) Field CM Traces A-L signs $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\) 3 5 17
255.2.a.a \(2\) \(2.036\) \(\Q(\sqrt{13}) \) None \(1\) \(-2\) \(-2\) \(0\) \(+\) \(+\) \(-\) \(q+\beta q^{2}-q^{3}+(1+\beta )q^{4}-q^{5}-\beta q^{6}+\cdots\)
255.2.a.b \(2\) \(2.036\) \(\Q(\sqrt{5}) \) None \(3\) \(-2\) \(2\) \(0\) \(+\) \(-\) \(+\) \(q+(1+\beta )q^{2}-q^{3}+3\beta q^{4}+q^{5}+(-1+\cdots)q^{6}+\cdots\)
255.2.a.c \(3\) \(2.036\) 3.3.229.1 None \(0\) \(3\) \(3\) \(4\) \(-\) \(-\) \(-\) \(q-\beta _{1}q^{2}+q^{3}+(1+\beta _{2})q^{4}+q^{5}-\beta _{1}q^{6}+\cdots\)
255.2.a.d \(4\) \(2.036\) 4.4.13768.1 None \(1\) \(4\) \(-4\) \(4\) \(-\) \(+\) \(+\) \(q-\beta _{3}q^{2}+q^{3}+(2-\beta _{1})q^{4}-q^{5}-\beta _{3}q^{6}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(255))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(255)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(15))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(17))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(51))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(85))\)\(^{\oplus 2}\)